python實現拉格朗日插值及作圖
本文實例為大傢分享瞭python實現拉格朗日插值及作圖,供大傢參考,具體內容如下
python代碼
import numpy as np import matplotlib.pyplot as plt X = input("x的值:").split(' ') Y = input("y的值:").split(' ') x = input("要預測的值:") print('\n') X = np.array(X).astype(np.float64) Y = np.array(Y).astype(np.float64) x = np.array(x).astype(np.float64) n = len(X) # 原函數 def fun(x): return np.sin(x) # 累乘函數 def T(x, i, X): T_i = 1 for x_i in X: if X[i] == x_i: continue T_i = T_i * (x-x_i) return T_i # 插值基函數 def P(i, x, X, Y): P_i = T(x, i, X)/T(X[i], i, X) * Y[i] return P_i # 計算預測值 def L(x, X, Y): result = 0 for i in range(n): result = result + P(i, x, X, Y) return result y = L(x, X, Y) print("預測結果:" + str(y) + '\n') print("誤差:" + str(fun(x) - y)) # 畫圖 X_n = np.linspace(0, 1, 50) Y_n = fun(X_n) x_n = np.linspace(0, 1, 50) y_n = L(x_n, X, Y) l1, = plt.plot(X_n, Y_n, label='theory') l2, = plt.plot(x_n, y_n, label='prediction',linestyle='--') plt.legend(handles=[l1,l2,],labels=['theory','prediction'], loc='best') plt.show()
代碼測試結果(輸入方式如圖所示):
以上就是本文的全部內容,希望對大傢的學習有所幫助,也希望大傢多多支持WalkonNet。
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